Finite Group Databasebeta

← #13182655

Subgroups — #13182655

Order 1760.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#713C211yesmaximal, characteristic
2C4×C11⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
3#11724975C211yesmaximal, characteristic, complemented
4C2×C11⋊AGL(1,𝔽5)—21no—
5C5×Q8×C11C411yescharacteristic, complemented
6C11×D20—21no—
7C11×D20C411yescharacteristic, complemented
8C4×D5×C11—21no—
9C4×D5×C11C2211yescharacteristic
10C11⋊#170—21no—
11#66901—51nomaximal, Hall
12C2×D5×C11—21no—
13C2×D5×C11D411yescharacteristic
14C11⋊AGL(1,𝔽5)—22no—
15C4×C5×C11—21no—
16C4×C5×C11C2×C411yescharacteristic
17C11×Dic5D411yescharacteristic
18C11×#41—51no—
19C4×Dic11—51no—
20#4318—51no—
21#4010—111nomaximal, Hall
22C2×C5×C11C22⋊C411yescharacteristic
23D5×C11—21no—
24D5×C11—41no—
25Q8×C11AGL(1,𝔽5)11yescharacteristic, complemented
26D4×C11—51no—
27D4×C11—101no—
28C2×C4×C11—51no—
29C2×C4×C11—101no—
30C2×Dic11—101no—
31C11⋊C8—101no—
32#713D1111yescharacteristic
33C4×AGL(1,𝔽5)—111no—
34#700—111no—
35C5×C11#10411yescharacteristic, complemented, Hall
36C22×C11—51no—
37C22×C11—101no—
38C4×C11—21no—
39C4×C11—51no—
40C4×C11C2×AGL(1,𝔽5)11yescharacteristic
41Dic11—102no—
42C2×AGL(1,𝔽5)—221no—
43C5×Q8Dic1111yescharacteristic, complemented
44D20—21no—
45D20Dic1111yescharacteristic, complemented
46C4×D5—21no—
47C4×D5C2×D1111yescharacteristic
48#170—221no—
49#104—551noSylow
50C2×C11—101no—
51C2×C11—201no—
52C2×C11C22⋊AGL(1,𝔽5)11yescharacteristic
53C2×D5—21no—
54C2×D5C22⋊D1111yescharacteristic
55AGL(1,𝔽5)—222no—
56C4×C5—21no—
57C4×C5C2×Dic1111yescharacteristic
58Dic5C22⋊D1111yescharacteristic
59#41—51no—
60M16—551no—
61C42—551no—
62C11#401011yescharacteristic, complemented, Sylow
63C2×C5C22⋊Dic1111yescharacteristic
64D5—21no—
65D5—41no—
66Q8C11⋊AGL(1,𝔽5)11yescharacteristic, complemented
67D4—51no—
68D4—101no—
69C2×C4—51no—
70C2×C4—101no—
71C2×C4—1101no—
72C8—1101no—
73C5#6690111yescharacteristic, complemented, Sylow
74C22—51no—
75C22—101no—
76C4—21no—
77C4—51no—
78C4—1102no—
79C4C2×C11⋊AGL(1,𝔽5)11yescharacteristic
80C2—101no—
81C2—201no—
82C2C22⋊(C11⋊AGL(1,𝔽5))11yescharacteristic
subgroupG/H
centerC2C22⋊(C11⋊AGL(1,𝔽5))
commutatorC4×C5×C11C2×C4
FrattiniC4C2×C11⋊AGL(1,𝔽5)
FittingC5×Q8×C11C4
socleC2×C5×C11C22⋊C4
prime radicalC11×#713C2
cosocleC4×D5×C11C22
hypercenterQ8C11⋊AGL(1,𝔽5)
hypocenterC5×C11#104
LCSG ▷ C4×C5×C11 ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2 ◁ C4 ◁ Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C4×C11⋊AGL(1,𝔽5)C2semidirect
3. #11724975C2semidirect
5. C5×Q8×C11C4semidirect
7. C11×D20C4semidirect
25. Q8×C11AGL(1,𝔽5)semidirect
35. C5×C11#104semidirect
43. C5×Q8Dic11semidirect
45. D20Dic11semidirect
62. C11#4010semidirect
66. Q8C11⋊AGL(1,𝔽5)semidirect
73. C5#66901semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#7132
C4×C11⋊AGL(1,𝔽5)2
#117249752
#669015
#401011